Universal codes of the natural numbers

Yuval Filmus

doi:https://doi.org/10.2168/LMCS-9(3:7)2013

Universal codes of the natural numbers

Research output: Contribution to journal › Article › peer-review

Abstract

A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how to construct effectively a code better than a given sequence of codes, in a certain precise sense. As an application, we prove that the existence of a scale of codes (a well-ordered set of codes which contains a code better than any given code) is independent of ZFC.

Original language	English
Article number	7
Journal	Logical Methods in Computer Science
Volume	9
Issue number	3
DOIs	https://doi.org/10.2168/LMCS-9(3:7)2013
State	Published - 29 Aug 2013
Externally published	Yes

Keywords

Kraft's inequality
Universal codes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

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https://doi.org/10.2168/LMCS-9(3:7)2013

Cite this

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Universal codes of the natural numbers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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